Building on work of Tyagi (2005), we present expressions for calculating the corner ion, edge-center ion, and face-center ion Madelung constants for bulk sodium chloride crystals. In [1], Crandall gives a historical overview of attempts to evaluate the Madelung constant for bulk ionic crystals. For sodium chloride he gave an expression for this in terms of the following series.

California’s failure in restructuring its electricity market has been interpreted to mean that “deregulation will not work.” A number of studies have pointed to flaws in the California experience that -if corrected -should allow restructuring to be successful. This study compares the California experience with the actual, successful experience of several other states/countries to identify what ...

It is of interest in cryptographic applications to obtain practical performance improvements for the discrete logarithm problem over prime fields Fp with p of size ≤ 500 bits. The linear sieve and the cubic sieve methods described in Coppersmith, Odlyzko and Schroeppel’s paper [3] are two practical algorithms for computing discrete logarithms over prime fields. The cubic sieve algorithm is asym...

where 0< T <∞, A(u) is a linear operator in X for each u in an open subset W of Y , G is a nonlinear Volterra operator defined from C([0,T ];X) into itself, and the nonlinear map f is defined from [0,T ]×Y ×Y into Y . By a strong solution to (1.1) on [0,T ′], 0< T ′ ≤ T , we mean an absolutely continuous function u from [0,T ′] into X such that u(t)∈W for almost every t ∈ [0,T ′] and satisfies ...